Identifying spatial invasion of pandemics on metapopulation networks via anatomizing arrival history

Spatial spread of infectious diseases among populations via the mobility of humans is highly stochastic and heterogeneous. Accurate forecast/mining of the spread process is often hard to be achieved by using statistical or mechanical models. Here we propose a new reverse problem, which aims to identify the stochastically spatial spread process itself from observable information regarding the arrival history of infectious cases in each subpopulation. We solved the problem by developing an efficient optimization algorithm based on dynamical programming, which comprises three procedures: i, anatomizing the whole spread process among all subpopulations into disjoint componential patches; ii, inferring the most probable invasion pathways underlying each patch via maximum likelihood estimation; iii, recovering the whole process by assembling the invasion pathways in each patch iteratively, without burdens in parameter calibrations and computer simulations. Based on the entropy theory, we introduced an identifiability measure to assess the difficulty level that an invasion pathway can be identified. Results on both artificial and empirical metapopulation networks show the robust performance in identifying actual invasion pathways driving pandemic spread.Comment: 14pages, 8 figures; Accepted by IEEE Transactions on Cybernetic

Deformation of Hypersurfaces Preserving the Moebius Metric and a Reduction Theorem

A hypersurface without umbilics in the n+1 dimensional Euclidean space is known to be determined by the Moebius metric and the Moebius second fundamental form up to a Moebius transformation when n>2. In this paper we consider Moebius rigidity for hypersurfaces and deformations of a hypersurface preserving the Moebius metric in the high dimensional case n>3. When the highest multiplicity of principal curvatures is less than n-2, the hypersurface is Moebius rigid. Deformable hypersurfaces and the possible deformations are also classified completely. In addition, we establish a Reduction Theorem characterizing the classical construction of cylinders, cones, and rotational hypersurfaces, which helps to find all the non-trivial deformable examples in our classification with wider application in the future.Comment: 51 pages. A mistake in the proof to Theorem 9.2 has been fixed. Accepted by Adv. in Mat